TSTP Solution File: ITP054^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : ITP054^1 : TPTP v8.2.0. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n022.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 20 22:16:05 EDT 2024

% Result   : Theorem 1.12s 0.64s
% Output   : CNFRefutation 1.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   43 (  12 unt;  10 typ;   0 def)
%            Number of atoms       :   72 (  15 equ;   0 cnn)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  226 (  34   ~;  28   |;   4   &; 153   @)
%                                         (   4 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Number of types       :    3 (   2 usr)
%            Number of type conns  :    7 (   7   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   37 (   0   ^  37   !;   0   ?;  37   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_sort1,type,
    nat: $tType ).

thf(decl_sort2,type,
    list_c1059388851t_unit: $tType ).

thf(decl_46,type,
    suc: nat > nat ).

thf(decl_47,type,
    size_s1406904903t_unit: list_c1059388851t_unit > nat ).

thf(decl_49,type,
    ord_less_nat: nat > nat > $o ).

thf(decl_50,type,
    ord_less_eq_nat: nat > nat > $o ).

thf(decl_54,type,
    fe: nat > list_c1059388851t_unit ).

thf(decl_57,type,
    index: nat ).

thf(decl_60,type,
    n1: nat ).

thf(decl_61,type,
    nMsg: nat ).

thf(fact_160_not__less__eq__eq,axiom,
    ! [X19: nat,X10: nat] :
      ( ~ ( ord_less_eq_nat @ X19 @ X10 )
    <=> ( ord_less_eq_nat @ ( suc @ X10 ) @ X19 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_not__less__eq__eq) ).

thf(conj_0,conjecture,
    ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ index ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(fact_13_nat__neq__iff,axiom,
    ! [X19: nat,X10: nat] :
      ( ( X19 != X10 )
    <=> ( ( ord_less_nat @ X19 @ X10 )
        | ( ord_less_nat @ X10 @ X19 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_nat__neq__iff) ).

thf(fact_166_less__or__eq__imp__le,axiom,
    ! [X19: nat,X10: nat] :
      ( ( ( ord_less_nat @ X19 @ X10 )
        | ( X19 = X10 ) )
     => ( ord_less_eq_nat @ X19 @ X10 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_less__or__eq__imp__le) ).

thf(fact_29_less__trans__Suc,axiom,
    ! [X28: nat,X29: nat,X35: nat] :
      ( ( ord_less_nat @ X28 @ X29 )
     => ( ( ord_less_nat @ X29 @ X35 )
       => ( ord_less_nat @ ( suc @ X28 ) @ X35 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_less__trans__Suc) ).

thf(fact_0_AssumpGreaterOccurrence_I1_J,axiom,
    ~ ( ord_less_nat @ nMsg @ n1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_AssumpGreaterOccurrence_I1_J) ).

thf(fact_1__092_060open_062nMsg_A_060_Alength_A_Ife_Aindex_J_092_060close_062,axiom,
    ord_less_nat @ nMsg @ ( size_s1406904903t_unit @ ( fe @ index ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__092_060open_062nMsg_A_060_Alength_A_Ife_Aindex_J_092_060close_062) ).

thf(c_0_7,plain,
    ! [X19: nat,X10: nat] :
      ( ~ ( ord_less_eq_nat @ X19 @ X10 )
    <=> ( ord_less_eq_nat @ ( suc @ X10 ) @ X19 ) ),
    inference(fof_simplification,[status(thm)],[fact_160_not__less__eq__eq]) ).

thf(c_0_8,negated_conjecture,
    ~ ( ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ index ) ) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).

thf(c_0_9,plain,
    ! [X19: nat,X10: nat] :
      ( ( X19 != X10 )
    <=> ( ( ord_less_nat @ X19 @ X10 )
        | ( ord_less_nat @ X10 @ X19 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_13_nat__neq__iff]) ).

thf(c_0_10,plain,
    ! [X1122: nat,X1123: nat] :
      ( ( ( ord_less_eq_nat @ X1122 @ X1123 )
        | ( ord_less_eq_nat @ ( suc @ X1123 ) @ X1122 ) )
      & ( ~ ( ord_less_eq_nat @ ( suc @ X1123 ) @ X1122 )
        | ~ ( ord_less_eq_nat @ X1122 @ X1123 ) ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).

thf(c_0_11,plain,
    ! [X1147: nat,X1148: nat] :
      ( ( ~ ( ord_less_nat @ X1147 @ X1148 )
        | ( ord_less_eq_nat @ X1147 @ X1148 ) )
      & ( ( X1147 != X1148 )
        | ( ord_less_eq_nat @ X1147 @ X1148 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_166_less__or__eq__imp__le])])])]) ).

thf(c_0_12,negated_conjecture,
    ~ ( ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ index ) ) ),
    inference(fof_nnf,[status(thm)],[c_0_8]) ).

thf(c_0_13,plain,
    ! [X758: nat,X759: nat] :
      ( ( ( X758 = X759 )
        | ( ord_less_nat @ X758 @ X759 )
        | ( ord_less_nat @ X759 @ X758 ) )
      & ( ~ ( ord_less_nat @ X758 @ X759 )
        | ( X758 != X759 ) )
      & ( ~ ( ord_less_nat @ X759 @ X758 )
        | ( X758 != X759 ) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).

thf(c_0_14,plain,
    ! [X10: nat,X9: nat] :
      ( ~ ( ord_less_eq_nat @ ( suc @ X9 ) @ X10 )
      | ~ ( ord_less_eq_nat @ X10 @ X9 ) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_15,plain,
    ! [X9: nat,X10: nat] :
      ( ( ord_less_eq_nat @ X9 @ X10 )
      | ~ ( ord_less_nat @ X9 @ X10 ) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

thf(c_0_16,plain,
    ! [X792: nat,X793: nat,X794: nat] :
      ( ~ ( ord_less_nat @ X792 @ X793 )
      | ~ ( ord_less_nat @ X793 @ X794 )
      | ( ord_less_nat @ ( suc @ X792 ) @ X794 ) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_29_less__trans__Suc])])]) ).

thf(c_0_17,negated_conjecture,
    ~ ( ord_less_nat @ n1 @ ( size_s1406904903t_unit @ ( fe @ index ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

thf(c_0_18,plain,
    ! [X10: nat,X9: nat] :
      ( ( X9 = X10 )
      | ( ord_less_nat @ X9 @ X10 )
      | ( ord_less_nat @ X10 @ X9 ) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

thf(c_0_19,plain,
    ! [X10: nat,X9: nat] :
      ( ~ ( ord_less_nat @ ( suc @ X9 ) @ X10 )
      | ~ ( ord_less_eq_nat @ X10 @ X9 ) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

thf(c_0_20,plain,
    ! [X9: nat,X10: nat,X19: nat] :
      ( ( ord_less_nat @ ( suc @ X9 ) @ X19 )
      | ~ ( ord_less_nat @ X9 @ X10 )
      | ~ ( ord_less_nat @ X10 @ X19 ) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

thf(c_0_21,negated_conjecture,
    ( ( n1
      = ( size_s1406904903t_unit @ ( fe @ index ) ) )
    | ( ord_less_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ n1 ) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

thf(c_0_22,plain,
    ! [X10: nat,X9: nat] :
      ( ~ ( ord_less_nat @ ( suc @ X9 ) @ X10 )
      | ~ ( ord_less_nat @ X10 @ X9 ) ),
    inference(spm,[status(thm)],[c_0_19,c_0_15]) ).

thf(c_0_23,negated_conjecture,
    ! [X9: nat] :
      ( ( n1
        = ( size_s1406904903t_unit @ ( fe @ index ) ) )
      | ( ord_less_nat @ ( suc @ X9 ) @ n1 )
      | ~ ( ord_less_nat @ X9 @ ( size_s1406904903t_unit @ ( fe @ index ) ) ) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

thf(c_0_24,plain,
    ~ ( ord_less_nat @ nMsg @ n1 ),
    inference(fof_simplification,[status(thm)],[fact_0_AssumpGreaterOccurrence_I1_J]) ).

thf(c_0_25,negated_conjecture,
    ! [X9: nat] :
      ( ( n1
        = ( size_s1406904903t_unit @ ( fe @ index ) ) )
      | ~ ( ord_less_nat @ X9 @ ( size_s1406904903t_unit @ ( fe @ index ) ) )
      | ~ ( ord_less_nat @ n1 @ X9 ) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

thf(c_0_26,plain,
    ord_less_nat @ nMsg @ ( size_s1406904903t_unit @ ( fe @ index ) ),
    inference(split_conjunct,[status(thm)],[fact_1__092_060open_062nMsg_A_060_Alength_A_Ife_Aindex_J_092_060close_062]) ).

thf(c_0_27,plain,
    ~ ( ord_less_nat @ nMsg @ n1 ),
    inference(fof_nnf,[status(thm)],[c_0_24]) ).

thf(c_0_28,negated_conjecture,
    ( ( n1
      = ( size_s1406904903t_unit @ ( fe @ index ) ) )
    | ~ ( ord_less_nat @ n1 @ nMsg ) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

thf(c_0_29,plain,
    ~ ( ord_less_nat @ nMsg @ n1 ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

thf(c_0_30,negated_conjecture,
    ( ( n1
      = ( size_s1406904903t_unit @ ( fe @ index ) ) )
    | ( n1 = nMsg ) ),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_18]),c_0_29]) ).

thf(c_0_31,negated_conjecture,
    ( n1
    = ( size_s1406904903t_unit @ ( fe @ index ) ) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_30]),c_0_26])]) ).

thf(c_0_32,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_31]),c_0_26])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14  % Problem    : ITP054^1 : TPTP v8.2.0. Released v7.5.0.
% 0.07/0.15  % Command    : run_E %s %d THM
% 0.13/0.36  % Computer : n022.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit   : 300
% 0.13/0.36  % WCLimit    : 300
% 0.13/0.36  % DateTime   : Sat May 18 16:03:07 EDT 2024
% 0.13/0.36  % CPUTime    : 
% 0.20/0.49  Running higher-order theorem proving
% 0.20/0.49  Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.12/0.64  # Version: 3.1.0-ho
% 1.12/0.64  # Preprocessing class: HSLSSMSMSSSNHFA.
% 1.12/0.64  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.12/0.64  # Starting new_ho_10 with 1500s (5) cores
% 1.12/0.64  # Starting new_ho_10_cnf2 with 300s (1) cores
% 1.12/0.64  # Starting full_lambda_6 with 300s (1) cores
% 1.12/0.64  # Starting full_lambda_9 with 300s (1) cores
% 1.12/0.64  # new_ho_10 with pid 17962 completed with status 0
% 1.12/0.64  # Result found by new_ho_10
% 1.12/0.64  # Preprocessing class: HSLSSMSMSSSNHFA.
% 1.12/0.64  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.12/0.64  # Starting new_ho_10 with 1500s (5) cores
% 1.12/0.64  # No SInE strategy applied
% 1.12/0.64  # Search class: HGHSM-FSLM31-MHFFFSBC
% 1.12/0.64  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.12/0.64  # Starting lpo1_lambda_fix with 811s (1) cores
% 1.12/0.64  # Starting new_ho_10 with 151s (1) cores
% 1.12/0.64  # Starting new_ho_10_unif with 136s (1) cores
% 1.12/0.64  # Starting ehoh_best3_fo with 136s (1) cores
% 1.12/0.64  # Starting new_ho_3 with 136s (1) cores
% 1.12/0.64  # lpo1_lambda_fix with pid 17968 completed with status 0
% 1.12/0.64  # Result found by lpo1_lambda_fix
% 1.12/0.64  # Preprocessing class: HSLSSMSMSSSNHFA.
% 1.12/0.64  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.12/0.64  # Starting new_ho_10 with 1500s (5) cores
% 1.12/0.64  # No SInE strategy applied
% 1.12/0.64  # Search class: HGHSM-FSLM31-MHFFFSBC
% 1.12/0.64  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 1.12/0.64  # Starting lpo1_lambda_fix with 811s (1) cores
% 1.12/0.64  # Preprocessing time       : 0.007 s
% 1.12/0.64  # Presaturation interreduction done
% 1.12/0.64  
% 1.12/0.64  # Proof found!
% 1.12/0.64  # SZS status Theorem
% 1.12/0.64  # SZS output start CNFRefutation
% See solution above
% 1.12/0.64  # Parsed axioms                        : 309
% 1.12/0.64  # Removed by relevancy pruning/SinE    : 0
% 1.12/0.64  # Initial clauses                      : 491
% 1.12/0.64  # Removed in clause preprocessing      : 67
% 1.12/0.64  # Initial clauses in saturation        : 424
% 1.12/0.64  # Processed clauses                    : 1393
% 1.12/0.64  # ...of these trivial                  : 26
% 1.12/0.64  # ...subsumed                          : 607
% 1.12/0.64  # ...remaining for further processing  : 760
% 1.12/0.64  # Other redundant clauses eliminated   : 78
% 1.12/0.64  # Clauses deleted for lack of memory   : 0
% 1.12/0.64  # Backward-subsumed                    : 1
% 1.12/0.64  # Backward-rewritten                   : 38
% 1.12/0.64  # Generated clauses                    : 3386
% 1.12/0.64  # ...of the previous two non-redundant : 2900
% 1.12/0.64  # ...aggressively subsumed             : 0
% 1.12/0.64  # Contextual simplify-reflections      : 1
% 1.12/0.64  # Paramodulations                      : 3200
% 1.12/0.64  # Factorizations                       : 5
% 1.12/0.64  # NegExts                              : 0
% 1.12/0.64  # Equation resolutions                 : 79
% 1.12/0.64  # Disequality decompositions           : 0
% 1.12/0.64  # Total rewrite steps                  : 791
% 1.12/0.64  # ...of those cached                   : 644
% 1.12/0.64  # Propositional unsat checks           : 0
% 1.12/0.64  #    Propositional check models        : 0
% 1.12/0.64  #    Propositional check unsatisfiable : 0
% 1.12/0.64  #    Propositional clauses             : 0
% 1.12/0.64  #    Propositional clauses after purity: 0
% 1.12/0.64  #    Propositional unsat core size     : 0
% 1.12/0.64  #    Propositional preprocessing time  : 0.000
% 1.12/0.64  #    Propositional encoding time       : 0.000
% 1.12/0.64  #    Propositional solver time         : 0.000
% 1.12/0.64  #    Success case prop preproc time    : 0.000
% 1.12/0.64  #    Success case prop encoding time   : 0.000
% 1.12/0.64  #    Success case prop solver time     : 0.000
% 1.12/0.64  # Current number of processed clauses  : 347
% 1.12/0.64  #    Positive orientable unit clauses  : 80
% 1.12/0.64  #    Positive unorientable unit clauses: 1
% 1.12/0.64  #    Negative unit clauses             : 66
% 1.12/0.64  #    Non-unit-clauses                  : 200
% 1.12/0.64  # Current number of unprocessed clauses: 2237
% 1.12/0.64  # ...number of literals in the above   : 5336
% 1.12/0.64  # Current number of archived formulas  : 0
% 1.12/0.64  # Current number of archived clauses   : 370
% 1.12/0.64  # Clause-clause subsumption calls (NU) : 24081
% 1.12/0.64  # Rec. Clause-clause subsumption calls : 12821
% 1.12/0.64  # Non-unit clause-clause subsumptions  : 218
% 1.12/0.64  # Unit Clause-clause subsumption calls : 1053
% 1.12/0.64  # Rewrite failures with RHS unbound    : 0
% 1.12/0.64  # BW rewrite match attempts            : 51
% 1.12/0.64  # BW rewrite match successes           : 23
% 1.12/0.64  # Condensation attempts                : 0
% 1.12/0.64  # Condensation successes               : 0
% 1.12/0.64  # Termbank termtop insertions          : 82365
% 1.12/0.64  # Search garbage collected termcells   : 9510
% 1.12/0.64  
% 1.12/0.64  # -------------------------------------------------
% 1.12/0.64  # User time                : 0.105 s
% 1.12/0.64  # System time              : 0.009 s
% 1.12/0.64  # Total time               : 0.114 s
% 1.12/0.64  # Maximum resident set size: 3996 pages
% 1.12/0.64  
% 1.12/0.64  # -------------------------------------------------
% 1.12/0.64  # User time                : 0.488 s
% 1.12/0.64  # System time              : 0.027 s
% 1.12/0.64  # Total time               : 0.515 s
% 1.12/0.64  # Maximum resident set size: 2200 pages
% 1.12/0.64  % E---3.1 exiting
% 1.12/0.64  % E exiting
%------------------------------------------------------------------------------